Simple theory of Rijke tube oscillation

A Simple theory of Rijke tube oscillation is presented based on mathematical realization of Rayleigh's qualitative explanation of the mechanism of Rijke tube. This is done assuming a single point of high temperature in an otherwise uniform tube and the sound source produced when cold air flows passing this point. The wave equation thus obtained is then rigorously solved, It is found that the Rijke tube oscillation is a feedback system. There is no feeback nor oscillation when the hot spot is at a node or antinode in the tube. The mean flow is necessary for the oscillation, the particle velocity of which is proportional to the mean velocity, and the ratio is proportional to the gauze temperature when the later is low and the feedback does not effect much the magnitude of the particle velocity. When the temperature is high, the feedback increases rapidly. Otherwise the growth is rather slow, when the mean flow or high temperature is first applied. The oscillations stop immediately when the mean flow is stopped. If the mean flow is controlled by a valve or a paddle at one end of the tube, an interesting sound is controlled by a valve or a paddle at one end of the tube, an interesting sound produced.